Combining PLS and GME to estimate Structural Equation Models

Structural Equation Models with Latent Variables (SEM-LV) are commonly used in frameworks, e.g. Customer Satisfaction (CS) analyses, where, once defined a construct by means of a path model, the interest is mainly focused on the estimation of the parameters indicating the strength of the relationships among the considered unobservable entities. Partial Least Squares (PLS) and LISREL are the estimation procedures usually considered (the first method performs the parameter estimation after a latent score reconstruction; while parameter estimates are directly obtained with the latter method from the covariance structure of the observed variables). Possible drawbacks may ensue from the presence of multi-collinearity in the following cases: in the outer model, only for the PLS algorithm, when constructs of the formative type are present; in the inner model, when some explicative latent variables are highly correlated, possibly due also to the correlations among the observable variables pertaining to different blocks. The Generalized Maximum Entropy (GME) method (Golan et al., 1996) represents a semi-parametric estimation method for the SEM (Ciavolino, Al Nasser, 2009) which works well in case of ill-behaved or nonlinear data. The GME approach considers the re-parameterization of the unknown parameters and the disturbance terms as a convex combination of the expected value of discrete random variables. The estimation is achieved by the maximization of the Shannon’s entropy function. Our proposal is to define a combined algorithm that use first PLS to estimate the latent variables and, then, GME to estimate the parameters in the inner and outer models, thus overcoming the possible presence of multi-collinearity. Moreover the algorithm will deal with the presence of missing values, by considering in the PLS step the procedure proposed by Boari et al. (2007). The behaviour of the proposed procedure is evaluated by using the ‘mobile’ data set, proposed by Tenenhaus et al. (2005) and available in Sanchez, Trinchera (2010), also simulating the presence of missing values.